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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)


Stable equivalence for some categories with radical square zero

Author: Idun Reiten
Journal: Trans. Amer. Math. Soc. 212 (1975), 333-345
MSC: Primary 18E05
MathSciNet review: 0382396
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Abstract: For certain abelian categories with radical square zero, containing artin rings with radical square zero as a special case, we give a way of constructing hereditary abelian categories stably equivalent to them, i.e. such that their categories modulo projectives are equivalent categories.

References [Enhancements On Off] (What's this?)

  • [1] M. Auslander, Representation dimension of artin algebras, Queen Mary College Notes, 1971.
  • [2] Maurice Auslander, Representation theory of Artin algebras. I, II, Comm. Algebra 1 (1974), 177–268; ibid. 1 (1974), 269–310. MR 0349747 (50 #2240)
  • [3] Maurice Auslander and Idun Reiten, Stable equivalence of Artin algebras, Proceedings of the Conference on Orders, Group Rings and Related Topics (Ohio State Univ., Columbus, Ohio, 1972) Springer, Berlin, 1973, pp. 8–71. Lecture Notes in Math., Vol. 353. MR 0335575 (49 #356)
  • [4] Maurice Auslander and Idun Reiten, Stable equivalence of dualizing 𝑅-varieties, Advances in Math. 12 (1974), 306–366. MR 0342505 (49 #7251)
  • [5] -, Stable equivalence of dualizing R-varieties. III: Dualizing R-varieties stably equivalent to hereditary R-varieties, Advances in Math. 17 (1975).
  • [6] Robert M. Fossum, Phillip A. Griffith, and Idun Reiten, Trivial extensions of abelian categories, Lecture Notes in Mathematics, Vol. 456, Springer-Verlag, Berlin-New York, 1975. Homological algebra of trivial extensions of abelian categories with applications to ring theory. MR 0389981 (52 #10810)

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PII: S 0002-9947(1975)0382396-2
Article copyright: © Copyright 1975 American Mathematical Society

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